Here’s a moderate Molinism. It has two parts.
1. Accept that subjunctive conditionals of free will (“F-conditionals”) have non-trivial truth values if their antecedents are sufficiently determinate, and God knows these truth values.
In this respect, the moderate Molinism is exactly like standard Molinism. Whatever qualifiers one wants to put on when F-conditionals have non-trivial truth values can be put in.
2. Deny that God can make use of his knowledge of an F-conditional with antecedent p as part of a reason for bringing it about that p.
Why go for (2)? In order to avoid the priority in the order of explanation argument: if God makes use of his knowledge of an F-conditional with antecedent p as part of a reason for for his bringing it about that p, then the truth of that F-conditional, as well as the truth of p, are explanatorily prior to the free action in the consequent, and hence the free action is entailed by facts explanatorily prior to it, which contradicts a plausible principle of alternate possibility.
If it’s logically impossible for anyone to make use of knowledge of F-conditionals with antecedent p as part of a reason for bringing it about that p, then this is not a problematic restriction on omnipotence.
Moreover, the idea that God has to bracket some of his knowledge of F-conditionals when making decisions seems quite plausible. For instance, plausibly, he has to bracket his knowledge of F-conditionals that, together with his knowledge of their antecedents, entail that he is going to do A, when he is deciding to do A.

Moreover, the idea that God has to bracket some of his knowledge of F-conditionals when making decisions seems quite plausible.
How would this ‘bracketing’ work? I presume that God can’t make himself forget things while deciding what world to actualize. Does he think the following sort of thing: “If I ignore the fact that people will freely do x, y, and z, which possible world would the best one for me to actualize? I will actualize that world, alpha, even though I foresee that (as a matter of fact) alpha is much worse than beta, in which people would have made much better decisions.”

Tim:
Yes, something like that. But God might add: “It would be nice to actualize beta on account of favorable F-conditional, but it is logically incoherent for me to do so–were I to actualize persons in situations just like those in beta, they would not be free, and that wouldn’t be beta.”

Alex–
Would this moderate Molinism be able to retain any of the explanatory benefits of standard modern Molinist accounts of providence? It seems to me like it would not, because all of the “tricks” that Molinists usually do are dependent on God’s knowledge of a given f-conditional being part of the reason that he brings about p. (God has to know the f-conditionals to arrange for prophecy, providence, prayer, etc.)
(Pardon me if this question makes no sense and I have totally misunderstood the position you articulated above.)